SafariFileEditViewHistory BookmarksWindowHelp74% (4)Sun 7:20 PMwebassign.netC Solution To Your Mat...W Z Score Table - Z Ta...Critical value (z*) for...(18) Calculating r an...W Z Score Table - Z Ta...A fall_exm_01 - PSYC 3..G when would i need t...The dean of the college of sciences want to know if engineering or physics majors do better in math. The dean collects the math scores for a sample of students from the college. Belowtime left.!..en Shot.09.03 PMare partial SPSS results:1:42:17Group StatisticsNMeanStd. DeviationStd. Error Meangroupengineeringphysics2.385141.800001082.00007.54247math1089.20005.69210en Shot...7.39 PMIndependent Samples TestLevene'sTest forEquality ofVariancesSig.t-test for Equality of MeansStd. Error 95% ConfidenceInterval of theDifferenceLower UpperFt dfSig.(2-tailed) Difference DifferenceMeanEqual variances assumed3.249.0882.9881matha) Compute the appropriate test statistic(s) to make a decision about Ho.Test Statistic =; Decision:---Select---b) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.[c) Compute the corresponding effect size(s) and indicate magnitude(s).If not appropriate, input and/or select "na" below.12; Magnitude:---Select---d) Make an interpretation based on the results.Physics majors score significantly less on math than engineering majors.Engineering majors score significantly less on math than physics majors.There is no significant math difference between engineering and physics majors.Submit AnswerOCT4étvWDOCX17O O O

Answered: The dean of the college of sciences…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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File
Edit
View
History Bookmarks
Window
Help
74% (4)
Sun 7:20 PM
webassign.net
C Solution To Your Mat...
W Z Score Table - Z Ta...
Critical value (z*) for...
(18) Calculating r an...
W Z Score Table - Z Ta...
A fall_exm_01 - PSYC 3..
G when would i need t...
The dean of the college of sciences want to know if engineering or physics majors do better in math. The dean collects the math scores for a sample of students from the college. Below
time left.!..
en Shot
.09.03 PM
are partial SPSS results:
1:42:17
Group Statistics
N
Mean
Std. Deviation
Std. Error Mean
group
engineering
physics
2.38514
1.80000
10
82.0000
7.54247
math
10
89.2000
5.69210
en Shot
...7.39 PM
Independent Samples Test
Levene's
Test for
Equality of
Variances
Sig.
t-test for Equality of Means
Std. Error 95% Confidence
Interval of the
Difference
Lower Upper
F
t df
Sig.
(2-tailed) Difference Difference
Mean
Equal variances assumed
3.249
.088
2.9881
math
a) Compute the appropriate test statistic(s) to make a decision about Ho.
Test Statistic =
; Decision:
---Select---
b) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[
c) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
12
; Magnitude:
---Select---
d) Make an interpretation based on the results.
Physics majors score significantly less on math than engineering majors.
Engineering majors score significantly less on math than physics majors.
There is no significant math difference between engineering and physics majors.
Submit Answer
OCT
4
étv
W
DOCX
17
O O O

Expert Solution

Step 1

Compute the test statistic:

The investigator is specifically interested to test whether the scores of engineering and physics majors are equal or not.

Denote µ₁ as the population mean score of engineering majors and µ₂ as the population mean score of physics majors.

Null hypothesis:

H₀ : μ₁ = μ₂

That is, there is no significant difference between the mean score of engineering majors and physics majors.

Alternative hypothesis:

H₁ : μ₁ ≠ μ₂

That is, there is a significant difference between the mean score of engineering majors and physics majors.

In order to test the hypothesis regarding the significant difference between the means of two independent samples, when the population standard deviations are unknown an independent sample t-test is appropriate.

Pooled sample variance:

The standard deviation in the scores of engineering majors is s₁ = 7.5425,

The standard deviation in the scores of physics majors is s₂ = 5.6921.

The pooled sample variance is obtained as 44.6447 from the calculation given below:

$\begin{array}{rcl} s_{p}^{2} & = & \frac{(n_{1} - 1) s_{1}^{2} + (n_{2} - 1) s_{2}^{2}}{n_{1} + n_{2} - 2} \\ = & \frac{(10 - 1) \times {(7.5425)}^{2} + (10 - 1) \times {(5.6921)}^{2}}{10 + 10 - 2} \\ = & \frac{512.0038 + 291.60002}{18} \\ = & 44.6447 \end{array}$

Thus, the pooled sample variance is 44.6447.

Standard error:

The standard error of the difference of means is obtained as 2.9881 from the calculation given below:

$\begin{array}{rcl} S_{M - M_{2}} & = & s_{p} \times \sqrt{\frac{1}{n_{1}} + \frac{1}{n_{2}}} \\ = & \sqrt{44.6447} \times \sqrt{\frac{1}{10} + \frac{1}{10}} \\ = & 6.6817 \times 0.4472 \\ = & 2.9881 \end{array}$

Thus, the standard error of the difference of means is 2.9881.

Test statistic:

The test statistic is obtained as -2.4096 from the calculation given below:

$\begin{array}{rcl} t & = & \frac{M_{1} - M_{2}}{S_{M - M_{2}}} \\ = & \frac{82 - 89.2}{2.9881} \\ = & \frac{- 7.2}{2.9881} \\ = & - 2.4096 \end{array}$

Thus, the test statistic is -2.4096.

Critical value:

The level of significance is α = 0.05.

The critical value is obtained as ±2.1009 from the calculation given below:

$\begin{array}{rcl} L e v e l o f s i g n i f i c a n c e i s α & = & 0.05 \\ D e g r e e s o f f r e e d o m d . f & = & n_{1} + n_{2} - 2 \\ = & 10 + 10 - 2 \\ = & 18 \\ C r i t i c a l v a l u e \pm t_{0.025, 18} & = & \pm 2.1009 \end{array}$

Since, the t-distribution is symmetric, the two critical values are –t_(α/2) = -2.1009 and +t_(α/2) = +2.1009.

Decision rule:

Denote t as test statistic value and t_(α/2) as the critical value.

Decision rule based on critical approach:

If t ≤ –t_(α/2) (or) t ≥ t_(α/2), then reject the null hypothesis H₀.

If –t_(α/2) < t < t_(α/2), then fail to reject the null hypothesis H_0.

Conclusion based on critical value approach:

The test statistic value is -2.4096 and critical value is ±2.1009.

Here, t ≤ –t_(α/2). That is, -2.4096 (=t) < 2.1009 (= -t_(α/2)).

By the rejection rule, reject the null hypothesis H₀.

Therefore, there is a significant difference between the mean scores of engineering majors and physics majors.

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